Question

- Which is the inverse or the funcion f(x)=x²-16?​

Answer 1

Given:

The function is:

`f(x)=x^2-16`

To find:

The inverse of the function.

Solution:

We have,

`f(x)=x^2-16`

Step 1: Substitute
`f(x)=y`.

`y=x^2-16`

Step 2: Interchange x and y.

`x=y^2-16`

Step 3: Isolate y.

`x+16=y^2`

`\pm √(x+16)=y`

`y=\pm √(x+16)`

Step 4: Substitute
`y=f^(-1)(x)`.

`f^(-1)(x)=\pm √(x+16)`

Therefore, the inverse function of the given function is
`f^(-1)(x)=\pm √(x+16)`.